Question
Triangle EFG is rotated -90 degrees ( clockwise) to create triangle XYZ. Which of the following statements must be true?
Answers
Answered by
GPT-4o mini
When triangle EFG is rotated -90 degrees (clockwise), the following statements must generally be true regarding the resulting triangle XYZ:
1. **Orientation Change**: Triangle XYZ will have its vertices in a different orientation compared to triangle EFG. The transformation will change the order of the points.
2. **Size and Shape**: The size and shape of triangle XYZ will remain the same as triangle EFG. A rotation is a rigid transformation, meaning that distances and angles are preserved.
3. **Coordinates Transformation**: If the coordinates of points E, F, and G are known, the coordinates of points X, Y, and Z can be obtained through a specific transformation:
- If point E is at (x1, y1), F at (x2, y2), and G at (x3, y3), then after a -90 degree rotation, the new coordinates will be:
- X = (y1, -x1)
- Y = (y2, -x2)
- Z = (y3, -x3)
4. **Position**: The locations of the vertices of triangle XYZ will be positioned 90 degrees in the clockwise direction relative to triangle EFG.
If any specific statements or options are provided, please share them for a more tailored response!
1. **Orientation Change**: Triangle XYZ will have its vertices in a different orientation compared to triangle EFG. The transformation will change the order of the points.
2. **Size and Shape**: The size and shape of triangle XYZ will remain the same as triangle EFG. A rotation is a rigid transformation, meaning that distances and angles are preserved.
3. **Coordinates Transformation**: If the coordinates of points E, F, and G are known, the coordinates of points X, Y, and Z can be obtained through a specific transformation:
- If point E is at (x1, y1), F at (x2, y2), and G at (x3, y3), then after a -90 degree rotation, the new coordinates will be:
- X = (y1, -x1)
- Y = (y2, -x2)
- Z = (y3, -x3)
4. **Position**: The locations of the vertices of triangle XYZ will be positioned 90 degrees in the clockwise direction relative to triangle EFG.
If any specific statements or options are provided, please share them for a more tailored response!